Navigation systems can use a variety of different sensors to detect changes to the motion and orientation of an object. For example accelerometers, gyros and magnetometers are often used as are photodiodes. Accelerometers detect applied force, gyros detect rotation rates and magnetometers detect the Earth's magnetic field and photodiodes can be used to detect the sun. Thus magnetometers and/or photodiodes can be used to determine absolute orientation.
Inertial navigation systems, based on accelerometers and gyroscopes, can be used either on their own or together with other navigation systems such as GPS. Navigation/guidance of rockets and other munitions is often based on the use of micro-electro-mechanical (MEMS) sensors due to their small size and low-cost. The accuracy of these sensors is relatively poor and not sufficient to meet typical navigation requirements unless external sensors are used to estimate and correct the inertial sensor errors. Using additional aiding sensors in this way is the basis of what is known as ‘integrated navigation’.
Integrated navigation is usually based on an algorithmic technique known as Kalman Filtering, a process which blends data from the inertial sensors and external aiding sensors in an optimal way. For this technique to operate robustly, it has traditionally been understood that navigation errors must be maintained within certain limits at all times, else the linearity assumptions on which the Kalman filter is founded will not be valid and the integrated navigation solution may become grossly inaccurate. It is normally desired to avoid this situation by constraining navigation error growth during projectile flight.
When considering navigation Kalman filtering for applications involving rockets, missiles and other rotating platforms, initialising and maintaining an accurate roll (bank) angle presents the biggest challenge. An analysis of the problems associated with the use of inertial guidance technology in such applications is provided by J. S. Bird in “Inertial Sensor Performance Requirements for a Long Range Artillery Rocket” (DTIC ADA279936), with the conclusion that the roll gyro scale factor accuracy is critical and needs to be less than 5 parts-per-million (ppm).
Unfortunately, inexpensive low grade MEMS gyroscopes have a scale factor error of several thousand ppm. Using a gyroscope with a scale factor accuracy of less than 5 ppm would not be practical in terms of cost. Therefore there is a need for a system that can achieve the desired accuracy using inexpensive sensors with much lower scale factor accuracy.
The errors in gyroscope sensors are broadly divided into bias errors and scale factor errors. Although these and other errors are measured and removed as part of a factory calibration process, there will always be residual errors present when the sensors are actually used. These arise for a variety of reasons such as temperature and humidity changes, as well as other physical stresses affecting the unit. In general these errors may be different each time the unit is switched on.
As discussed in the above-referenced paper by J. S. Bird, in strapdown inertial navigation systems (i.e. those in which the inertial sensors are fixed to the body of the airframe as opposed to those in which the sensors are mounted on a gimballed platform that is free to rotate and so remain level at all times), one of the biggest problems comes from high roll rates. Typically roll rates for ballistic projectiles may be of the order of 10-20 full rotations per second, i.e. rotation rates of the order of a few thousand degrees per second. Therefore with a typical roll rate scale factor error of 1000 ppm, the roll angle (bank angle) calculated from this gyro would accumulate an error of a few degrees per second. For a typical projectile range of 30 to 60 km and a typical flight time of 1 to 2 minutes, this error quickly mounts up to be unacceptable.
Gyro bias error can readily be compensated immediately prior to use by averaging a series of readings while the gyro is known to be in a non-rotating state, e.g. prior to launch in the case of a projectile such as a rocket or missile. However, the scale factor error is rate-dependent and may not be measured and corrected whilst stationary. This suggests the need for a scale factor error correction process which operates in-flight, in a wholly self-contained fashion.
Alternative techniques which have been used in attempts to maintain roll accuracy include the use of non-inertial sensor aiding such as magnetometer, light sensor, GPS and/or thermopiles. These approaches add complexity and cost and introduce additional performance constraints. See for example “Attitude Determination with Magnetometers for un-Launched Munitions”, M. J. Wilson, DTIC ADA425992; and “On the Viability of Magnetometer-Based Projectile Orientation Measurements”, T. E. Harkins, DTIC ADA474475.
“Position Estimation for Projectiles Using Low-cost Sensors and Flight Dynamics” by L. D. Fairfax and F. E. Fresconi (DTIC ADA560811) describes another solution to this problem for gun-launched mortars which relies upon a multi-state Extended Kalman Filter to estimate position and velocity, but roll angle is determined via additional attitude aiding. This technique is applied to an application with a more benign roll rate profile than a typical artillery rocket.
U.S. Pat. No. 8,047,070 describes a process for estimating the roll angle of a gun-launched projectile. U.S. Pat. No. 8,047,070 uses body angular rate data as its measurements, as opposed to derived Euler angles. It also does not estimate or correct the roll rate scale factor error and it does not operate to preserve elevation and heading accuracy.
GPS-aided systems are frequently deployed in munitions applications and a navigation Kalman filter normally features in the guidance/control solution. Most applications involve a period of ballistic or near-ballistic flight, and this environment has some unique characteristics which affect the observability of some key Kalman filter error states. As discussed above, the use of low-cost MEMS sensors means that navigation errors develop rapidly in the absence of GPS aiding, and the process of navigation initialisation is often complicated by the fact that it must be carried out in flight, on a spinning platform where the roll angle is completely unknown or known only with very poor accuracy.
Broadly speaking, guided munitions can be divided into two different types, guided rockets and artillery/mortars.
Earlier techniques developed by the present applicant were concerned with minimising the Kalman filter error growth in guided rocket applications. In guided rocket applications, integrated navigation is generally initialised on the ground, while the projectile is still in the launch tube. The navigation equipment is powered up and the mission planning computer is able to transfer a full vector of data that accurately initialises all of the navigation variables. Integrated navigation continues uninterrupted from pre-launch, through the launch event and into the flight phase. The main difficulty with these applications is that significant spinning motion is often present, and the low-cost MEMS gyro measuring the spin motion generally has a sufficiently large scale factor error that all knowledge of platform roll angle is lost by the time GPS aiding is available, usually some 10-15 seconds into the flight. This problem led to earlier development of techniques such as those described in United Kingdom patent publication no. 2526508, United Kingdom patent publication no. 2534833, and United Kingdom patent application no. 1610747.6 for constraining roll angle error growth during the early flight phase, the aim being to maintain attitude errors within certain limits that would allow the navigation Kalman filter to correct the solution and achieve orderly convergence once GPS was acquired.
Mortar and artillery applications have different requirements from guided rockets. On these platforms the navigation equipment may be pre-programmed with parameters such as launch position, launch velocity and initial heading and elevation angles, after which the equipment will normally remain powered-off until shortly after launch. Trajectories will usually involve spinning motion, and even if the roll angle is known prior to launch (which is not normally the case), it will be completely unknown at the point of power on. Whilst all the other navigation variables may be known with acceptable accuracy at this time, the unknown roll angle will usually preclude initialisation of the integrated navigation function.
The conventional solution to this problem is to deploy a bespoke ‘upfinding’ function that runs prior to navigation initialisation. Using data from inertial sensors, or from other sensors such as magnetometers or photodiodes, a conventional upfinder produces an initial estimate of roll angle and this is used to start the integrated navigation process. The upfinding function is sometimes described as ‘coarse alignment’, and this function is invariably implemented as a standalone process, external to the navigation Kalman filter. Once coarse alignment is complete, the roll angle estimate is used to initialise integrated navigation and the system transitions to a ‘fine alignment’ mode. However, as described above, such ‘upfinding’ processes and associated additional sensors add cost and complexity to the system.